{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What impact does the first 5 days have on the prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from plotnine import *\n",
    "\n",
    "import statsmodels.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n",
    "\n",
    "from plotnine import *\n",
    "import plotnine.options\n",
    "plotnine.options.figure_size = (16,8)\n",
    "\n",
    "import warnings\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)\n",
    "\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>track_id</th>\n",
       "      <th>streams_cumsum_5</th>\n",
       "      <th>pop_5</th>\n",
       "      <th>all_streams_cumsum</th>\n",
       "      <th>cum_sum_after_pop_5</th>\n",
       "      <th>log_cum_sum_after_pop_5</th>\n",
       "      <th>log_cum_sum_5</th>\n",
       "      <th>log_all_streams_cumsum</th>\n",
       "      <th>fraction_of_stream_pre_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>00kzys67XYXiB31cSP5jfo</td>\n",
       "      <td>58838</td>\n",
       "      <td>40.0</td>\n",
       "      <td>473673</td>\n",
       "      <td>414835</td>\n",
       "      <td>12.935636</td>\n",
       "      <td>10.982543</td>\n",
       "      <td>13.068272</td>\n",
       "      <td>0.110492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>00mc2RHScEYMEFlc7FRGaK</td>\n",
       "      <td>4976</td>\n",
       "      <td>26.0</td>\n",
       "      <td>93919</td>\n",
       "      <td>88943</td>\n",
       "      <td>11.395751</td>\n",
       "      <td>8.512382</td>\n",
       "      <td>11.450188</td>\n",
       "      <td>0.050316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>04HzRAn3BJaIvmhpvc1GVT</td>\n",
       "      <td>190131</td>\n",
       "      <td>51.0</td>\n",
       "      <td>1426517</td>\n",
       "      <td>1236386</td>\n",
       "      <td>14.027703</td>\n",
       "      <td>12.155469</td>\n",
       "      <td>14.170746</td>\n",
       "      <td>0.117608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>04qrVtScdD4IBGSL5q6yEv</td>\n",
       "      <td>131276</td>\n",
       "      <td>47.0</td>\n",
       "      <td>2637515</td>\n",
       "      <td>2506239</td>\n",
       "      <td>14.734294</td>\n",
       "      <td>11.785057</td>\n",
       "      <td>14.785348</td>\n",
       "      <td>0.047413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>09aaq7feVx9Jykdw0f00QU</td>\n",
       "      <td>168800</td>\n",
       "      <td>50.0</td>\n",
       "      <td>1371458</td>\n",
       "      <td>1202658</td>\n",
       "      <td>14.000045</td>\n",
       "      <td>12.036470</td>\n",
       "      <td>14.131385</td>\n",
       "      <td>0.109592</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 track_id  streams_cumsum_5  pop_5  all_streams_cumsum  \\\n",
       "0  00kzys67XYXiB31cSP5jfo             58838   40.0              473673   \n",
       "1  00mc2RHScEYMEFlc7FRGaK              4976   26.0               93919   \n",
       "2  04HzRAn3BJaIvmhpvc1GVT            190131   51.0             1426517   \n",
       "3  04qrVtScdD4IBGSL5q6yEv            131276   47.0             2637515   \n",
       "4  09aaq7feVx9Jykdw0f00QU            168800   50.0             1371458   \n",
       "\n",
       "   cum_sum_after_pop_5  log_cum_sum_after_pop_5  log_cum_sum_5  \\\n",
       "0               414835                12.935636      10.982543   \n",
       "1                88943                11.395751       8.512382   \n",
       "2              1236386                14.027703      12.155469   \n",
       "3              2506239                14.734294      11.785057   \n",
       "4              1202658                14.000045      12.036470   \n",
       "\n",
       "   log_all_streams_cumsum  fraction_of_stream_pre_5  \n",
       "0               13.068272                  0.110492  \n",
       "1               11.450188                  0.050316  \n",
       "2               14.170746                  0.117608  \n",
       "3               14.785348                  0.047413  \n",
       "4               14.131385                  0.109592  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp = pd.read_feather('../data/archive_as_of_friday_20_july/streams_post_day_5_pop.feather')\n",
    "sp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DQ80tt9ySY90//vgj1307k9Pdmy644AL/Pa5du3bmlVdeMS+88IJJTk42ksyYMWPy/XnZ97s1a9bkurxjx45Gktm0aVOOZR9++KGRZCZNmuRvK1u2rKlYsWKu23rooYeMJPPVV1/lWHa6/T5Z69atTWJiYo42SWbs2LEB7a+88oqRZGbOnHnG7WbfgxMSEszBgwf97WlpaaZJkybG6XQGnM+5Zc7PPX/ChAlGkrn//vtzrH/iz60T7zk+n88MGTLESDLDhg0zPp/vjPt1+PBhEx4ebtq2bRvQ7vP5TGJioqldu7a/raDnb/b59O6775q//vrL7N2712zYsMF/Hp14rVx22WXGsizz2WefBWxj9OjRRpJ5/PHH/W35PTanMmXKFNO3b18zd+5c8/bbb5tJkyb57zcnX/cAgNKJYdQAAL+kpCR98803uvfeexUWFqY33nhDDz74oFq2bKlatWrpo48+yvc2hw4dmmOo4YoVK7R371716tVLqamp2rdvn/9fq1atFBERETAjbEREhP+/MzIydODAAe3bt0/t2rWT1+vNdXjfvffeG9BLJXt27cqVK+foedG6dWtlZWX5hzGWK1fOPxT7xJ5gwZA9XDO3HjTZM9qezZDOs/1MSQoLCwv4TDsynujOO+9UTEyM/7XD4dCVV16pPXv26MiRI3nahtfrVVxcnOLi4pSQkKB27drpt99+08SJE3XXXXcFrLtw4UKFh4fr5ptvDjgX9+3bpy5duiglJUWfffaZJGnJkiXy+XwaNmxYwPcTGxurgQMHFnjfhw4dqnfffVft27fX9u3b9dxzz6lPnz6qUaOGOnfuHDB0Mi9iY2MDhnZmy88+S4HXYGpqqvbv3y+Xy6WLL744oFdsNofDoX/+858BbdkzJffs2VPR0dH+9kqVKik5OVk//fSTvy37+L/++utBH6KZ/ciEWrVqadmyZbrlllvUp08frVu3TtHR0XriiSd06NChoH7m6a6p7GeXnnwNnu56PXn9YHI4HDkmemrbtq2k3B9BcCr33HNPwHNdw8LCNGTIEHm93jP2As7PPX/hwoWKiIjQ448/nuu+nCw9PV033XSTnn76aU2fPl0TJkw44zNvJSkqKkpdu3bVxx9/HPD84lWrVumXX37x92qUgnf+duzYUXFxcYqPj1fz5s310UcfqWfPnv5e+H/99ZfWrFmja665Jkcv2GHDhikiIkJvvPFGju0W5NhI0j//+U/NmjVLvXr1UqdOnTRkyBB99913qlmzpv79738X+PnOAIDij2IjACBAYmKipk2bpl9++UV//PGH3nnnHd12223auXOnunbt6h+Kmld16tTJ0fbjjz9KOv4LT3ZBKPtfxYoVdfToUf3xxx/+9Y8dO6aHHnrI//zE8uXLKy4uTnfccYck5TppRvaQ8BPFxMScsl2S9u/fL0mqXr26Ro8erY8//lhVqlRRo0aNNHDgwLMqtp4sezhbRkZGjmUZGRkyxgR9Ap3TfaYkpaWlBXymHRlPlNsxyh76nH2MzsThcGj58uVavny5Fi9erO7duyslJSXX2Xd//PFHpaWlqWrVqjnOx+xZt7PPx23btknKfcbVf/zjH3nbwTPo0KGD3nvvPR0+fFibN2/WzJkzVb9+fb399tunnF35VGrWrCmn05mjPT/7LEnffvutunTpoqioKEVFRalChQqKi4vTsmXLcr3+qlSpkmMCoOzr7FTX4InH9t5771WzZs00aNAgxcTEqG3bthozZox27NiRr/3PTfajBHr16hVQZCpfvrw6d+6stLQ0bdiwocCfc6LTXVPZzwA8+Ro83fV68vrBlNuxy+/1J+V+jWS3nennSH7u+Vu3blWdOnUCCpSn8+CDD2rx4sV6/vnn8/0Hgl69esnn82nhwoX+tvnz58vhcPizScE7f6dMmaLly5fr448/1hdffKH9+/dr3rx5/kmetm/fLin3e0+ZMmVUs2ZN/z3rRAU5NqcSGRmp+++/X1lZWVq+fPlZbQMAUHLwzEYAwClVrFhRHTt2VMeOHVWtWjU9+eSTevXVV/XII4/keRu5/ULs8/kkSWPGjFGzZs1yfd+JPdtuvfVWvf322+rbt69atWqlChUqyOVy6auvvtKIESP82ztRbgWW07VLCihEPfroo7rjjju0bNkyrV27VosXL9aMGTPUuXNnLVmyJE89YXKTPclObj0/fvvtt4B1guV0n5n9uSd+ph0ZT5TXY3Q6lmX5J4SRpG7duik0NFTDhw/XBRdcELDM5/MpOjpaixcvPuX28lJIzGu2vHI6nUpOTlZycrJ69Oihf/zjH/roo4+0e/fuPH//pypI5Wefd+3apZYtW6ps2bJ66KGHVLduXUVERMjhcGjcuHFauXJlrtlPt1+5OfH7i4mJ0Weffab169dr+fLlWrt2rUaPHq3Ro0drwYIFuvnmm0+5/TOpVq2avv/+e1WuXDnHsuy2gs76fbITr6nzzz8/YFlu11RCQoK2bt2qjIyMHD0cC/saDMb1dyZnun+ezT0/r7p06aI33nhDkyZNUvv27XM9D07lyiuvVLVq1TR//nyNGDFCR44c0RtvvKGrrroq4HgE6/xt2rRpwGzUJ8s+Hmf78yg3BdlW9jNH89sDGwBQ8lBsBADkSfbEBtm/6Epn/0tJdm/HsLCwgKJPbg4fPuzv0fX8888HLDtx2GVhSExM1IABAzRgwAB5PB716NFDr776qtauXesfEppf2cXV9evX51iW3XaqAuzZqlSpkqpXr66vv/5aaWlpAZPE7N69W7t27QqY7MWOjOfCU089pcWLF2vw4MH67rvv/EMs69Spo82bN6tx48a5Th5zopo1a0o6PqP5yQXITZs2FU5wHe+N17hxY+3YsSNHcfhs5GeflyxZotTUVC1dulRXXHFFwLJ//etfBcpxOg6HQy1btvQXW3755RddeOGFevjhhwtUbGzevLnef/997dq1K8eyX3/9VZL8s34HS7NmzfTcc89p/fr1/iHJ2bKvqYsuuihg/c2bN2vDhg1q3bp1jvUTExMLZXKYYNq0aZM6d+6co03633WUm/ze8+vUqaOtW7fq6NGjeerdePnll6tfv37q0KGDWrVqpY8//ljVq1fPyy7J4XCoR48eGjt2rD7//HP9+OOPOnr0aMAQ6hPXLYzz90TZ3+P333+fY1laWpq2b9+uWrVq5Vh2tsfmTLKPT3x8/FlvAwBQMjCMGgDgt3r16lM+B2zJkiWSAodfZQ/lym8voGuuuUaVKlXShAkTcn0mosfj8W8zuyB0co+a1NRUTZ48OV+fm1eHDx/O8Zwtl8ulhg0bSipYr6caNWqoRYsW+uSTTwKeO+bxeDR16lRFRkbm+CUwGHr06KG0tDQ9++yzAe3Z32GPHj1sz1jY4uLidO+992rTpk0BwyCzC63Dhw/PtefWicOJu3TpIsuyNHHiRGVmZvrbDxw4oGeeeaZA+dLT03PtJShJf/75p9atWyeXy6XatWv728uWLXtW52N+9jm7p9vJ633wwQf6z3/+k+/PzovcekZVr15dcXFxBe51eNttt8nlcmnmzJkBx3DXrl166623FBsbq0suuaRAn3GyLl26KDIyUi+88IJSUlL87bt379brr7+uli1bqkaNGv727Ovx5Hvc22+/rW3btgVcr0XVjBkzAp59mZGRocmTJ8vpdOq666475fvye8+//fbbdfToUT366KM5lp2qB2TLli21YsUK7d+/X61atfIPR86L7MLi/PnzNX/+fEVHR6tr164B6xTm+XuiuLg4XXbZZfrwww9zXIuTJk3SkSNH1K1btxzvO9tjIx3/OZDbcPq//vpLEydOVFhYWI6COgCg9KFnIwDA7+mnn9aqVavUsWNHNWnSRDExMdq3b5/ee+89ffLJJ6pfv77uvPNO//rNmzfX9OnTdc8996hDhw5yu926+OKLA35pzk2ZMmW0YMECde7cWeeff77uvPNOJScnKzU1VT///LPefPNNjR8/Xr169VJkZKTatWunl156SaGhobr44ou1Z88ezZ49O+i9j7KtWrVK/fr10/XXX6/k5GRFR0frhx9+0HPPPafq1avn6N2VX1OnTlWrVq10zTXX6P7771eFChX00ksv6YsvvtDMmTMDhpBLx4em/fLLLzl++X7iiScCXu/cudPflpiYGFCQGD58uBYvXqzhw4dr586datSokdasWaP58+ere/fuuvLKKwuUsbgYNmyYpk+frscee0y33nqrXC6Xrr/+evXr10+zZs3yP5uwUqVK+v333/Xll1/q/fff9xefa9euraFDh2rixIlq0aKFunfvrvT0dM2ePVtVqlTRnj17cnzmqY7fydLT03XllVeqbt26uvbaa5WcnCyHw6Ft27ZpwYIF+uOPPzRq1CjFxsb639O8eXOtWLFC48ePV/Xq1WVZlm655ZYzfg/52edrr71WERER6tGjhwYOHKgKFSroq6++0ssvv6wGDRrou+++y88hyJP+/fvr119/1TXXXKPExER5PB69/fbb2rJlS47JS/KrZs2aGjlypB599FG1aNHCX6x65plnlJaWppkzZwYMP583b5569+6tkSNHatSoUf72Tz/9VJ9++qn/vyXpxRdf1OrVqyUdLxgmJiZKOj6sNntyohYtWuiuu+5SZmampk2bJp/Pp6lTpwZkvOqqq9S9e3e98sor6tSpkzp37qydO3dqypQpqlu3rh544IECfQfnQsWKFXXRRRfpzjvvVEhIiF5++WX997//1SOPPHLanxH5vecPHjxY7733nqZMmaKvv/5a7du3V2RkpLZu3aqPPvoo115/0vGepKtXr1bbtm39PRyTk5PPuF+1a9fWpZdeqoULF+rIkSPq379/jmdcFub5e7Lse/UVV1yhAQMGKCkpSWvXrtXLL7+sRo0aaciQITnec7bHRpKOHDmihIQEdevWTQ0aNFBsbKx+/vlnzZ49WwcOHNC0adPyNTQdAFBCnfsJsAEARdWGDRv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\n",
      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223363300469049284)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(sp, aes('pop_5', 'log_cum_sum_after_pop_5')) + geom_point() + geom_point(aes('pop_5', 'log_all_streams_cumsum'), color = \"red\") + ggtitle('Streams [0,100] in Red, Streams [6,100] in black vs Pop 5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8736385778159)>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(sp, aes('log_cum_sum_5', 'log_cum_sum_after_pop_5')) + geom_point() + geom_abline(slope=1) + ggtitle('Streams[6,100] vs Streams[0,5]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223363300469107505)>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ggplot(sp, aes('pop_5','fraction_of_stream_pre_5')) + geom_point()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>log_cum_sum_after_pop_5</td> <th>  R-squared:         </th> <td>   0.470</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                      <td>OLS</td>           <th>  Adj. R-squared:    </th> <td>   0.459</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                <td>Least Squares</td>      <th>  F-statistic:       </th> <td>   45.20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>                <td>Wed, 05 Sep 2018</td>     <th>  Prob (F-statistic):</th> <td>1.49e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                    <td>17:01:39</td>         <th>  Log-Likelihood:    </th> <td> -70.518</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>         <td>    53</td>          <th>  AIC:               </th> <td>   145.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>             <td>    51</td>          <th>  BIC:               </th> <td>   149.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>                 <td>     1</td>          <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>nonrobust</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    9.8972</td> <td>    0.501</td> <td>   19.761</td> <td> 0.000</td> <td>    8.892</td> <td>   10.903</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pop_5</th> <td>    0.0745</td> <td>    0.011</td> <td>    6.723</td> <td> 0.000</td> <td>    0.052</td> <td>    0.097</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.888</td> <th>  Durbin-Watson:     </th> <td>   2.334</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.641</td> <th>  Jarque-Bera (JB):  </th> <td>   0.972</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.241</td> <th>  Prob(JB):          </th> <td>   0.615</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.544</td> <th>  Cond. No.          </th> <td>    177.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               OLS Regression Results                              \n",
       "===================================================================================\n",
       "Dep. Variable:     log_cum_sum_after_pop_5   R-squared:                       0.470\n",
       "Model:                                 OLS   Adj. R-squared:                  0.459\n",
       "Method:                      Least Squares   F-statistic:                     45.20\n",
       "Date:                     Wed, 05 Sep 2018   Prob (F-statistic):           1.49e-08\n",
       "Time:                             17:01:39   Log-Likelihood:                -70.518\n",
       "No. Observations:                       53   AIC:                             145.0\n",
       "Df Residuals:                           51   BIC:                             149.0\n",
       "Df Model:                                1                                         \n",
       "Covariance Type:                 nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          9.8972      0.501     19.761      0.000       8.892      10.903\n",
       "pop_5          0.0745      0.011      6.723      0.000       0.052       0.097\n",
       "==============================================================================\n",
       "Omnibus:                        0.888   Durbin-Watson:                   2.334\n",
       "Prob(Omnibus):                  0.641   Jarque-Bera (JB):                0.972\n",
       "Skew:                          -0.241   Prob(JB):                        0.615\n",
       "Kurtosis:                       2.544   Cond. No.                         177.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(sp['log_cum_sum_after_pop_5'], sm.add_constant(sp['pop_5']))\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>track_id</th>\n",
       "      <th>cumsum_day_1</th>\n",
       "      <th>cumsum_day_100</th>\n",
       "      <th>cumsum_2to100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>00kzys67XYXiB31cSP5jfo</td>\n",
       "      <td>26282</td>\n",
       "      <td>473673</td>\n",
       "      <td>447391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>00mc2RHScEYMEFlc7FRGaK</td>\n",
       "      <td>2141</td>\n",
       "      <td>93919</td>\n",
       "      <td>91778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>04HzRAn3BJaIvmhpvc1GVT</td>\n",
       "      <td>95386</td>\n",
       "      <td>1426517</td>\n",
       "      <td>1331131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>04qrVtScdD4IBGSL5q6yEv</td>\n",
       "      <td>54710</td>\n",
       "      <td>2637515</td>\n",
       "      <td>2582805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>09aaq7feVx9Jykdw0f00QU</td>\n",
       "      <td>58813</td>\n",
       "      <td>1371458</td>\n",
       "      <td>1312645</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 track_id  cumsum_day_1  cumsum_day_100  cumsum_2to100\n",
       "0  00kzys67XYXiB31cSP5jfo         26282          473673         447391\n",
       "1  00mc2RHScEYMEFlc7FRGaK          2141           93919          91778\n",
       "2  04HzRAn3BJaIvmhpvc1GVT         95386         1426517        1331131\n",
       "3  04qrVtScdD4IBGSL5q6yEv         54710         2637515        2582805\n",
       "4  09aaq7feVx9Jykdw0f00QU         58813         1371458        1312645"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "streams_1_100 = pd.read_feather('../data/archive_as_of_friday_20_july/streams_1_100.feather')\n",
    "streams_1_100.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (-9223363300469275893)>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ggplot(streams_1_100, aes('cumsum_day_1', 'cumsum_2to100')) + \n",
    "geom_point() + \n",
    "scale_x_log10() + \n",
    "scale_y_log10())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IAAAAACAJZSQAAAAAkIQyEgAAAABIQhkJAAAAACTxP+YlzaBAuZD8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8736385176945)>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ggplot(streams_1_100, aes('cumsum_day_1', 'cumsum_2to100')) + \n",
    "geom_point() + \n",
    "scale_x_log10() + \n",
    "scale_y_log10() + coord_cartesian(xlim=[1, 1e7], ylim=[1,1e7]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>cumsum_2to100</td>  <th>  R-squared:         </th> <td>   0.537</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.528</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   59.06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 05 Sep 2018</td> <th>  Prob (F-statistic):</th> <td>4.53e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>17:04:41</td>     <th>  Log-Likelihood:    </th> <td> -65.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    53</td>      <th>  AIC:               </th> <td>   134.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    51</td>      <th>  BIC:               </th> <td>   138.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>        <td>    5.8636</td> <td>    0.967</td> <td>    6.063</td> <td> 0.000</td> <td>    3.922</td> <td>    7.805</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cumsum_day_1</th> <td>    0.6982</td> <td>    0.091</td> <td>    7.685</td> <td> 0.000</td> <td>    0.516</td> <td>    0.881</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.598</td> <th>  Durbin-Watson:     </th> <td>   2.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.165</td> <th>  Jarque-Bera (JB):  </th> <td>   2.138</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.257</td> <th>  Prob(JB):          </th> <td>   0.343</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.161</td> <th>  Cond. No.          </th> <td>    89.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:          cumsum_2to100   R-squared:                       0.537\n",
       "Model:                            OLS   Adj. R-squared:                  0.528\n",
       "Method:                 Least Squares   F-statistic:                     59.06\n",
       "Date:                Wed, 05 Sep 2018   Prob (F-statistic):           4.53e-10\n",
       "Time:                        17:04:41   Log-Likelihood:                -65.431\n",
       "No. Observations:                  53   AIC:                             134.9\n",
       "Df Residuals:                      51   BIC:                             138.8\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "================================================================================\n",
       "                   coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------\n",
       "const            5.8636      0.967      6.063      0.000       3.922       7.805\n",
       "cumsum_day_1     0.6982      0.091      7.685      0.000       0.516       0.881\n",
       "==============================================================================\n",
       "Omnibus:                        3.598   Durbin-Watson:                   2.162\n",
       "Prob(Omnibus):                  0.165   Jarque-Bera (JB):                2.138\n",
       "Skew:                          -0.257   Prob(JB):                        0.343\n",
       "Kurtosis:                       2.161   Cond. No.                         89.2\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(np.log(streams_1_100['cumsum_2to100']), sm.add_constant(np.log(streams_1_100['cumsum_day_1'])))\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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